Moving and staying together without a leader

@article{Grgoire2003MovingAS,
  title={Moving and staying together without a leader},
  author={Guillaume Gr{\'e}goire and Hugues Chat{\'e} and Yuhai Tu},
  journal={Physica D: Nonlinear Phenomena},
  year={2003},
  volume={181},
  pages={157-170}
}
Collective motion of self-propelled particles interacting without cohesion.
TLDR
The onset of collective motion in Vicsek-style self-propelled particle models in two and three space dimensions is studied in detail and shown to be discontinuous (first-order-like), and the properties of the ordered, collectively moving phase are investigated.
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Boltzmann and hydrodynamic description for self-propelled particles.
TLDR
A homogeneous spontaneous motion emerges below a transition line in the noise-density plane, and is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.
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  • 2013
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This work uses a variant of the Vicsek model that includes pairwise repulsive interactions to describe the collective behaviour of self-propelled particles and suggests that in certain parameter ranges they observe collectively migrating clusters that arrange in an approximately hexagonal way.
Collective Dynamics of Pedestrians with No Fixed Destination
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TLDR
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Onset of collective and cohesive motion.
TLDR
It is found that this phase transition, in two space dimensions, is always discontinuous, including for the minimal model of Vicsek et al. for which a nontrivial critical point was previously advocated.
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